Collective gyromagnetic ratio from density dependent hartree-fock calculations: (II). Odd nuclei

The collective gyromagnetic ratio and moment of inertia of deformed odd-proton and oddneutron axially symmetric nuclei have been calculated in the cranking approximation using wave functions obtained with the Skyrme force SIII. Good agreement with experiment is found for g_R. Our parameter-free cranking results are better than those of Prior, Boehm and Nilsson where effective charges were used. The cranking formula leads to better results than the projection method (in which one simply takes the expectation value of the relevant operator in the deformed HF ground state, neglecting corrections of relative order 1/〈J²〉. In particular, the cranking results follow nicely the exceptionally large/small g_R for the odd-proton/neutron nuclei around mass 153–167.     

原子核的转动惯量和gR因子

基于Inglis的推转模型(cranking model),我们利用Nilsson波函数对原子核转动惯量及集体运动g_R,因子作了仔细的计算,计算结果相当满意,无论在数值上,或是随不同原子核的变化,以及随不同激发带的变化上都和实验结果相近。其原因可能是由于选择了一个较恰当的、含有强自旋轨道耦合的轴对称自洽场。     

Effective dynamic moment of inertia of 118Xe and 130Ba

The effective moment of inertia J_eff⁽²⁾ of ¹¹⁸Xe and ¹³⁰Ba has been measured using sum-spectrometer techniques. The data are discussed using arguments based on particle alignments and results of cranking calculations. J_band⁽²⁾ and J_eff⁽²⁾ are compared in order to estimate the contribution of particle alignments to the total increase in angular momentum.     

The moment of inertia at the saddle point of low energy fission of even-even nuclei

We use the molecular model of low energy fission, which describes the nucleus by two interacting fragments, to calculate the moment of inertia for U²³⁶ in the cranking approximation including BCS theory. We show that the moment of inertia at the saddle point:

1. depends almost linearly on the fragment distance.
2. is influenced only very weakly by the pairing constant and by the fragment deformations.
3. shows, as a function of the distribution of mass between the two fragments (A ₁ ,A ₂ ), a minimum near the magic configurationA ₁=132,Z ₁=50 and depends in this mass region strongly on the term structure near the Fermi energy.
4. is approximately that of a rigid body.

     

Influence of quadrupole pairing on backbending

The influence of the different quadrupole pairing forces ∝ Y_2m (m = 0, 1, 2) and the spin-dependent particle-hole force on backbending (BB) is studied. A cranked Hartree-Fock-Bogoliubov approach with particle number projection before the variation of the important degrees of freedom is used. To discuss the numerical results qualitatively perturbative formulas for the moment of inertia and the gap parameters are given. The results are the following: (i) The quadrupole pairing Y₂₁ is not affecting the backbending. (ii) The Y₂₀ pairing is reducing the moment of inertia at low angular momenta by about 20 %. This just cancels the increase of the moment of inertia by Y₂₁ pairing at low angular momenta, (iii) The Y₂₁ and Y₂₀ pairing together shift the backbending point to higher angular momenta and better agreement with the experimental data. (iv) A spin-dependent ph force does not affect the moment of inertia at low angular momentum. But above backbending it reduces the moment of inertia by about 13 % to the correct experimental value if a strength parameter adapted in ²⁰⁸Pb is used.     

A Study for Nuclei 166Hf94—170Hf98 Using Cranking Shell Model with PNC Method

The properties of the band in even nuclei of ¹⁶⁶Hf₉₄—¹⁷⁰Hf₉₈ are investigated using cranking shell model with PNC method. The band crossing frequency, the interaction intensity between yrast and yrare bands, the aligned momentum, and the moment of inertia are calculated. The comparison between the calculation and experimental data shows a good agreement with each other if Lund systematic parameter is used for the Nilsson potential.     

Backbending in theN=96 isotones

The backbending in the even-even,N=96 isotones can be quantitatively accounted for by the rotation-alignment of the spins of neutrons in i 13/2 orbits, as shown by comparing the aligned angular momentum and relative Routhian for thes-bands in these isotones and for the i 13/2 bands in the corresponding isotopes withN=91. The influence of protons on this backbending situation is shown to be indirect, acting through a change of the nuclear deformation, which yields a change of the moment of inertia of the g.s. band and of the non-rigid character of the rotation. The experimental data on theN=96 and 97 isotones are in reasonable agreement with cranking model calculations. Possible reasons for the inhibition of backbending in the h 9/2 proton bands in the odd-Z, N=96 isotones, all related to a change of deformation, are presented.     

g Factors for high-spin states of238U

Calculations of the g-factor and the moment of inertia J for high-spin states of²³⁸U are performed using the model which is based on the cranking Hartree-Fock-Bogolyubov (CHFB) theory. Importance of the state-dependent pairing force on 3(ω²) is investigated.     

HIGH-ORDER CRANKING CALCULATION IN THE INTERACTING BOSON MODEL AND INTERACTING BOSONFERMION MODEL

Considering that the IBM and IBFM cranking calculations in the lowest order of angular frequency can give reasonably good estimates for the moment of inertia,we extend them to study the dependence of the moment of inertia on the higher order terms.We find that the analytic expressions for the correction terms can be derived.Numerical calculations for ¹⁵⁴Gd and ¹⁶¹Er are performed and compared with experiment.The Hamiltonian is taken from a microscopic approach.Calculated results show that the properties of higher order terms depend on the deformation of rotating system but the correction yields only limited effect when ω is small.     

Study on 222–226Th Isotopes in the Cranking Framework

The yrast spectra, quadrupole moments, quadrupole deformation parameters (β ₂), non-axiality parameters (γ), root mean-square radii for protons and neutrons, occupation probabilities, moment of inertia (I), and B(E2) transition probabilities are calculated for ^222–226Th in the cranked Hartree–Bogoliubov framework. The calculations employ a quadrupole-quadrupole plus pairing model of residual interaction operating in a reasonably large valence space outside the ¹⁶⁴Pb core. Our calculations reproduce qualitatively the observed yrast spectra in ^222–226Th up to spin 20⁺. The calculated results indicate that the non-axiality parameter decreases as one moves along the yrast states. The observed increase in deformation from ²²²Th to ²²⁶Th is due to the increase in the occupation of low-k components of $(2g_{9/2})_{\pi }$ and $(1j_{{15/2}})_{\nu }$ orbits. The model parameters reproduce not only the moment of inertia, deformation, and transition probabilities but also the proton and neutron pairing gaps and are the most appropriate for cranking studies in this region.     

Triaxial superdeformation in 163Lu

High-spin states in ¹⁶³Lu have been investigated using the Euroball spectrometer array. The previously known superdeformed band has been extended at low and high energies, and its connection to the normal-deformed states has been established. From its decay the mixing amplitude and interaction strength between superdeformed and normal states are derived. In addition, a new band with a similar dynamic moment of inertia has been found. The experimental results are compared to cranking calculations which suggest that the superdeformed bands in this mass region correspond to shapes with a pronounced triaxiality (γ≈±20°).     

Band head spin assignment of superdeformed bands in 86Zr

Two parameter expressions for rotational spectra viz. variable moment of inertia (VMI), ab formula and three parameter Harris ω² expansion are used to assign the band head spins (I₀) of four rotational superdeformed bands in ⁸⁶Zr. The least-squares fitting method is employed to obtain the band head spins of these four bands in the A~80 mass region. Model parameters are extracted by fitting of intraband γ-ray energies, so as to obtain a minimum root-mean-square (rms) deviation between the calculated and the observed transition energies. The calculated transition energies are found to depend sensitively on the assigned spins. Whenever an accurate band head spin is assigned, the calculated transition energies are in agreement with the experimental transition energies. The dynamic moment of inertia is also extracted and its variation with rotational frequency is investigated. Since a better agreement of band head spin with experimental results is found using the VMI model, it is a more powerful tool than the ab formula and Harris ω² expansion.     

Expansion of moment of inertia at high temperature

The moment of inertia of hot nuclei is expanded in powers of the rotational frequency ω. The first two expansion coefficients are determined for temperatures above T_c, where the equilibrium shape is spherical at ω = 0. It is shown how the moment of inertia varies with temperature, rotational frequency, proton number, and neutron number.     

Studies of the nuclear inertia in fission and heavy-ion reactions

On the basis of the non-self-consistent cranking model we study some aspects of the nuclear inertia of interest in fission and heavy-ion reactions. First, we consider in the adiabatic limit the inertia for a doubly closed-shell nucleus in a deformed spheroidal harmonic-oscillator single-particle potential plus a small perturbation. When expressed in terms of a coordinate that describes the deformation of the nuclear matter distribution, the inertia for small oscillations about a spherical shape is exactly equal to the incompressible, irrotational value. For large distortions it deviates from the incompressible, irrotational value by up to about ±1 % away from level crossings. Second, in order to study the dependence of the inertia upon a level crossing, we consider in detail two levels of the above system. This is done both in the adiabatic limit and for large collective velocities. At level crossings the adiabatic inertia relative to the deformation of the matter distribution diverges as 1/|ΔV|, where |ΔV| is the magnitude of the perturbation. However, for large collective velocities the contribution to the inertia from a level crossing is less than 4|ΔV|r²_m, where r_m is the collective velocity of the matter distribution. Although we have not considered the effect of large velocities on the remaining levels of the many-body system or the effect of a statistical ensemble of states, some of our results suggest that for high excitation energies and moderately large collective velocities the nuclear inertia approaches approximately the irrotational value.     

THE MOMENT OF INERTIA IN THE INTERACTING BOSON-FERMION MODEL

For a system described by the interacting boson-fermion model (IBFM),we construct the intrinsic states and study the moment of inertia of deformed odd-A nuclei in terms of the selfconsistent cranking calculation.An approximate analytic method for the energy spectrum is presented in the general cases where the IBFM Hamiltonian does not have dynamical symmetry.The rationality of this method is also discussed by taking ^153,155,157Eu isotopes as examples.     

Hf高自族态推转壳模型PNC方法研究

用推转壳模型ＰＮＣ方法研究了１６６Ｈｆ９４－１７０Ｈｆ９８核，计算了这三个核晕带和次晕带间的带交叉频率、带间互作用强度、顺排角动量和转动惯量等，并与实验值作了比较，结果表明在Ｎｉｌｓｓｏｎ势参数完全按照Ｌｕｎｄ系统学选取的情况下，理论计算值与实验值符合得较好．     

Influence of the weakly interacting light U boson on the properties of massive protoneutron stars

Considering the octet baryons in relativistic mean field theory and selecting entropy per baryon S=l,we calculate and discuss the influence of U bosons on the equation of state,mass-radius,moment of inertia and gravitational redshift of massive protoneutron stars(PNSs).The effective coupling constant gu of U bosons and nucleons is selected from 0 to 70 GeV~(-2).The results indicate that U bosons will stiffen the equation of state(EOS).The influence of U bosons on the pressure is more obvious at low density than high density,while the influence of U bosons on the energy density is more obvious at high density than low density.The U bosons play a significant role in increasing the maximum mass and radius of PNS.When the value of gu changes from 0 to 70 GeV~(-2),the maximum mass of a massive PNS increases from 2.11M_⊙ to 2.58M_⊙,and the radius of a PNS corresponding to PSR J0348+0432 increases from 13.71 km to 24.35 km.The U bosons will increase the moment of inertia and decrease the gravitational redshift of a PNS.For the PNS of the massive PSR J0348+0432,the radius and moment of inertia vary directly with gu,and the gravitational redshift varies approximately inversely with gu.     

On oblate-prolate transition in the ground state rotational band of light mercury isotopes

The transition from an oblate to a prolate shape in the ground state band of even mass Hg isotopes and in the ground states of the chain of odd mass Hg isotopes are studied. The shape is found by minimizing the deformation energy which is calculated by means of Strutinsky's shell correction method. The rotational energy corresponds to the axialsymmetric rotator. The moment of inertia is calculated with the help of the cranking model. Pairing and hexadecupole deformation are included. The results are in good agreement with the available experimental data.